calculus
posted by angie .
how do I graph this using the first and second derivative and three sign charts.
i have to label the inflection point, extreme values and the intercepts also.
f(x)= x^36x^2

slope = 3 x^2 12 x =3 x (x4)
second derivative (curvature)
= 6 x  12
so the slope is 0 at x = 0 and at x = 4
at x = 0
is that a min or a max or in inflection point?
second derivative = 12
That is a maximum, starts down from there
at x = 4 is that a min or a max or an inflection point?
second derivative = +12
so that is a minimum, starts up fro there. 
Oh, intercepts
y = x^36x^2
0 = x^2 (x6)
bounced off x axis at x = 0
crossed x axis at x = 6
Respond to this Question
Similar Questions

calc
one more question!! what values of c deos the polynomial f(x) = x^4 + cx^3 + x^2 have two inflection points? 
increasing decreasing and more
How to analytically find the intervals on which the function y = 2x^4  4x^2 + 1 is 1)increasing 2)decreasing 3)concave up 4)concave down Also find any local extreme values and inflection points. Thanks. (1) The function is increasing … 
calc.
I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: … 
calculus ..>steve
Given a function f(x)2/3x^3+5/2x^23x. a) Find i. The inflection point. ii. The yintercept and xintercept. b) Sketch the graph of f(x). i have already try it..but i don't understand.. which graph that is true.. the first or second … 
Calculus
Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection … 
Calculus
Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection … 
Calculus answer check
A brand new stock is also called an initial public offering. This model predicts the percent overvaluation of a stock as R(t)=9t((t3)^3/2.718) where is the overvaluation in percent and t is the time in months after the initial issue. … 
Calculus
For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine where the function is increasing and decreasing, where it is concave up and concave down, and any points of inflection. I understand this is using the first and second … 
Differential Calculus
Determine all local extrema, concavity and inflection point/s for y = 2cos(x) in (0, 2Pi). Test by both First Derivative Test and Second Derivative Test and sketch the graph. 
Calculus
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 0. Which of the following statements is false?